1 An Objectivist Argument for Thirdism

The literature on the Sleeping Beauty problem has been dominated by Bayesians.1 Even those authors who are not Bayesians2 have addressed the problem without using much of the rich machinery available to objective probability theorists. We show that the objective probability theorist has a very simple argument for thirdism. Objective Probability Bayesians take “definite ” or “single-case ” probabilities to be basic. Definite probabilities attach to closed formulas or propositions. We write them here using small caps: PROB(P) and PROB(P/Q). Most objective probability theories begin instead with “indefinite ” or “general ” probabilities (sometimes called “statistical probabilities”). Indefinite probabilities attach to open formulas or propositions. We write indefinite probabilities using lower case “prob ” and free variables: prob(Bx/Ax). The indefinite probability of an A being a B is not about any particular A, but rather about the property of being an A. In this respect, its logical form is the same as that of relative frequencies. For instance, we might talk about the probability of a human baby being female. That probability is about human babies in general — not about individuals. If we examine a baby and determine conclusively that she is female, then the definite probability of her being female is 1, bu